Custom deck building for DC?

Hi - new to the game (enjoy it greatly) and was curious if there are any rule variants (or perhaps in tournament rules) where you would construct your own deck to compete with another player? Similar to a living card game - the ability to customize your own deck across the DC sets and then compete?

Or are the big tournaments simply "we're playing this game" and then the random superhero draw?

Deck Building games aren't really designed for prebuilding individual player decks. The entire concept is that the players have to build their decks as they play and cycle them repeatedly to progress. None of the card abilities really work towards using a pre-established deck at the start of the game.

You COULD prebuild a main deck that everyone would play from though. That's quite common.

I've tried to do character or 'family' themed main decks like a Batman family deck and a Green Lantern themed deck. The problem often lies in balancing the types and costs of cards suited to the theme.